# Scientific Notation Chapter Questions Scientific Notation Chapter Questions

1. What is the purpose of scientific notation?
1. When would you use scientific notation?
1. How do you convert between standard form and scientific notation?
1. How do you compare numbers when they are written in scientific notation?
1. How do you multiply and divide numbers in scientific notation?
1. How do you add and subtract numbers in scientific notation with the same exponents?
1. How do you add and subtract numbers in scientific notation with different exponents?

Scientific Notation Chapter Problems

Purpose of Scientific Notation

Classwork

1. Express the following powers of ten in standard form:
2. 101 =
3. 102 =
4. 103 =
5. 104 =
6. 105 =
1. Express the following answers as powers of 10.
2. 103 x 105 =
3. 1011 x 106 =
4. 1012 x 10-8 =
5. 10-4 x 10-7 =
6. 10-9 x 103 =

Homework

1. Express the following powers of ten in standard form:
2. 109 =
3. 108 =
4. 107 =
5. 106 =
6. 105 =
1. Express the following answers as powers of 10.
2. 102 x 104 =
3. 103 x 1012 =
4. 10-6 x 108 =
5. 10-3 x 10-9 =
6. 10-7 x 102 =

How to Write Numbers in Scientific Notation

Classwork

1. Which of the following are correctly written in scientific notation?
2. 3.0 x 105
3. 0.56 x 109
4. 0.103 x 103
5. 15 x 10-5
6. 5.6 x 10-8
7. 4 x 102
8. 0.345 x 10-2
9. Write each number in scientific notation.
10. 13,030,000
11. 418,000
12. 25,024,000
13. 4,500,000
14. 20,000
15. 870,000,000
16. 0.0325
17. 0.0000564
18. 0.00092
19. 0.001002
20. 0.00006
21. 0.00965784
1. Write each number in scientific notation.
2. Lightest blue whale: 418,000 lb
3. Thinnest glass: 0.00098 in.
4. Lightest bird egg:0.0128 oz.
5. Diameter of thinnest copper wire: 0.0005 in.
6. Mass of Earth’s atmosphere: 5,700,000,000,000,000 tons
7. Amount of gold in Earth’s crust: 120,000,000,000,000 metric tons

Homework

1. Which of the following are correctly written in scientific notation?
2. 0.5 x 104
3. 15 x 109
4. 3.5567 x 10-7
5. 1 x 106
6. 5.04 x 10-4
7. 0.05 x 10-2
8. 6.788432 x 108
1. Write each number in scientific notation.
2. 4,566,000
3. 17,000,300
4. 35,000
5. 1,078,000,000
6. 4,560,700
7. 943,000,000,000
8. 0.000578
9. 0.004598732
10. 0.000000558744
11. 0.0001000358
12. 0.00045805
13. 0.000000000000851
1. Write each number in scientific notation.
2. Mass of smallest insect, a parasitic wasp: 0.00000492 g
3. Speed of light: 300,000,000 m/sec
4. Mass of a dust particle:0.000000000753 kg
5. Distance from Earth to the Sun is approximately: 149,600,000 km
6. Earth’s circumference: 40,000,000 m
7. Distance between the Sun and Neptune: 4,497,100,000 km

Converting to Standard Form

Classwork

1. Write each number in standard form.
2. Temperature at the Sun’s core: 1.55 x 106 K
3. Lowest temperature ever in a lab: 2 x 10-11 K
4. Radius of the neon atom is about 3.5 x 10-11 meters
5. Radius of Earth’s orbit: 1.5 x 1011 meters
6. Avagadro’s number: 6.022 x 1023
7. Weight of a paper clip: 1.1 x 10-3 lb.
1. Write each number in standard form:
2. 7.5 x 105
3. 9.765 x 10-10
4. 1.27 x 10-8
5. 4.56 x 106
6. 3.0 x 10-6
7. 6.785168 x 108
8. 8.00045 x 10-4

1. Which number represents the number 2.3E-4?
a. 230,000
b. 23,000
c. 0.00023
d. 0.000023
2. Which number represents the number 6.29E10
a. 6,290,000,000,000
b. 62,900,000,000
c. 0.000000000629
d. 0.0000000000629

Homework

1. Write each number in standard form.
2. Width of a human hair:7.5 x 10-5 meter
3. Distance between Jupiter and the Sun: 4.836 x 1011
4. Charge on a Proton/Electron: 1.602176 x 10-19 C
5. Faraday constant: 9.649 x 104
6. Number of bits on a computer hard disk (as of 2010): 1 x 1013 GB
7. Wavelength of green light: 5.5 x 10-7 m
1. Write each number in standard form:
2. 8.445 x 10-4
3. 5.256544 x 109
4. 1.0 x 10-5
5. 7.45207 x 108
6. 2.67 x 10-5
7. 6.0005 x 106
8. 4.00896 x 10-3

1. Which number represents 6.05E7?
a. 60,500,000
b. 6,050,000,000
c. 0.0000000605
d. 0.000000605
2. Which number represents 9.83E-10
a. 9,830,000,000,000
b. 98,300,000,000
c. 0.0000000000983
d. 0.000000000983

Magnitude

Classwork

Write each of the following in scientific notation first, and then indicate the order of magnitude.

1. 367______
2. 1819.74______
3. 5200600 ______
4. .00917 ______
5. .0363 ______
6. .000001 ______
7. If M = 624,619,430,000 find the smallest power of 10 that will exceed M.
8. If M = 84,973 find the smallest power of 10 that will exceed M.
9. If M = 17.196419 find the smallest power of 10 that will exceed M.

Homework

1. 7677 ______
2. 2489.02 ______
3. 4174381 ______
4. .00689 ______
5. .0002 ______
6. .000051 ______
7. If M = 8924600043.67 find the smallest power of 10 that will exceed M.
8. If M = 3.162 find the smallest power of 10 that will exceed M.
9. If M = 4536 find the smallest power of 10 that will exceed M.

Comparing Numbers in Scientific Notation

Classwork

1. Place the appropriate inequality symbols between the following numbers:
2. 9.5 x 1048.2 x 107
3. 6.231 x 1072.34 x 103
4. 4.567 x 10 -27.32 x 105
5. 1.0 x 10-42.0 x 10-5
6. 5.66 x 10-76.54 x 10-9
7. 8.32 x 10-67.236 x 10-11
8. 4.52 x 1047.532 x 104
9. 6.5431 x 1086.32 x 108
10. 3.5 x 10-61.0 x 10-6
11. 4.509 x 10103.45 x 1010
1. Order the following sets of numbers from least to greatest.
2. 2.3 x 1034.5 x 1057.8 x 1021.3 x 104
3. 4.0 x 1095.0 x 1076.0 x 10107.0 x 105
4. 4.3 x 1047.5 x 10-21.9 x 1063.3 x 10-4
5. 2.5 x 10-125.5 x 10-258.2 x 1029.5 x 10-9
6. 5.4 x 1043.2 x 1049.9x 1042.1 x 104
7. 9.2 x 10-58.2 x 10-69.2 x 10-68.2 x 10-5

Homework

1. Place the appropriate inequality symbols between the following numbers:
2. 3.2 x 1064.2 x 109
3. 5.41 x 1046.54 x 107
4. 9.875 x 10-81.0345 x 108
5. 3.0 x 10-64.0 x 10-9
6. 4.35 x 10-47.21 x 10-3
7. 8.369 x 10-84.1 x 10-13
8. 3.98 x 1065.98 x 106
9. 1.65 x 1041.56 x 104
10. 8.3 x 10-83.0 x 10-8
11. 6.8999 x 10157.43 x 1015
1. Order the following sets of numbers from least to greatest.
2. 4.7 x 1038.9 x 1076.5 x 1056.7 x 104
3. 2.0 x 10123.0 x 1064.0 x 1085.0 x 103
4. 9.9 x 1055.7 x 10-31.8 x 10-74.4 x 106
5. 1.9 x 10-103.6 x 10-69.7 x 1034.5 x 10-23
6. 9.3 x 1085.0 x 1088.9x 1086.7 x 108
7. 5.5 x 10-74.5 x 10-79.0 x 10-72.7 x 10-7

Multiplying and Dividing with Scientific Notation

Classwork

1. Evaluate the following. Express the result in scientific notation.
2. (3.0 x 10-5)(2.0 x 109)=
3. (4.0 x 103)(5.0 x 105)=
4. (6.0 x 10-5)(3.0 x 108)=
5. (1.5 x 108)(3.2 x 10-4)=
6. (2.7 x 10-3)(1.1 x 108)=
7. (1.3 x 10-4)(2.0 x 10-6)=
8. (8.4 x 106)÷(2.0 x 103)=
9. (9.3 x 108)÷(3.0 x 10-2)=
10. (5.4 x 1010)÷(2.0 x 104)=
11. =
12. =
13. =
1. A tiny space inside a computer chip has been measured to be 2.56 x 10-6 meters wide, 1.4 x 10-7 meters long, and 2.75 x 10-4 meters high. What is its volume?
1. In one year about 478 billion telephone calls were placed by 145 million United States telephone subscribers. What was the average number of calls placed per subscriber?

Homework

1. Evaluate the following. Express the result in scientific notation.
2. (3.0 x 10-5)(3.0 x 108)=
3. (4.0 x 102)(4.0 x 107)=
4. (7.0 x 10-3)(6.0 x 106)=
5. (1.2x 107)(2.2 x 10-3)=
6. (2.0 x 10-4)(7.1 x 109)=
7. (4.4 x 10-7)(3.0 x 10-3)=
8. (6.6x 108)÷(2.0 x 104)=
9. (2.7x 106)÷(3.0 x 10-4)=
10. (7.5x 1012)÷(2.0 x 105)=
11. =
12. =
13. =
1. A tiny space inside another computer chip has been measured to be 3.5 x 10-7 meters wide, 1.8 x 10-8 meters long, and 6.45 x 10-5 meters high. What is its volume?
1. The point on a pin has a diameter of approximately 1 x 10-4 meters. If a neon atom has a diameter of about 7.0 x 10-11 meters, about how many neon atoms could fit across the diameter of the point of a pin?

Adding and Subtracting with Scientific Notation

Classwork

1. Evaluate the following. Express the result in scientific notation.
2. (2.1 x 105) + (2.7 x 105)=
3. (3.7 x 108) + (4.6 x 108)=
4. (6.8 x 10-6) - (3.4 x 10-6)=
5. (6.1 x 106) + (3.5 x 107)=
6. (8.5 x 1010) - (1.5 x 109)=
1. What is the difference between the mass of Earth (5.98 x 1024 kg) and the mass of Venus (4.87 x 1024 kg)?
1. What is the difference between the mass of Jupiter (1.90 x 1027 kg) and the mass of Saturn (5.69 x 1026 kg)?

Homework

1. Evaluate the following. Express the result in scientific notation.
2. (5.8x 109) + (3.1 x 109)=
3. (3.5x 106) + (5.8 x 106)=
4. (7.5x 10-4) - (4.2 x 10-4)=
5. (5.4x 107) + (2.2 x 108)=
6. (6.5x 1012) - (3.4 x 1011)=
1. What is the difference between the mass of Mars (6.42 x 1023 kg)and the mass of Mercury (3.3 x 1023 kg)?
1. What is the difference between the mass of Earth (5.98 x 1024 kg) and the mass of Mars (6.42 x 1023 kg)?

Scientific Notation Unit Review

Multiple Choice– Choose the correct answer for each question.

1. Which of the following powers of 10 is not correctly written in standard form?
2. 105 = 100,000
3. 103 = 1,000
4. 106 = 1,000,000
5. 101 = 1
1. Express the following as a power of ten: 10 x 107 =
2. 108
3. 107
4. 106
5. 1008
1. Express the following as a power of ten: 10-5 x 10-10 =
2. 1050
3. 10-50
4. 10-15
5. 1015
1. The temperature at the Sun’s core can reach as high as 13,600,000 kelvins. What is this number correctly written in scientific notation?
2. 136 x 105
3. 1.36 x 107
4. 1.36 x 105
5. 1.36 x 106
1. What is the number .00000002 correctly written in scientific notation?
2. 2.0 x 10-8
3. 2.0 x 10-9
4. 0.2 x 10-8
5. 2.0 x 10-10
1. What is 4.56 x 105 in standard form?
2. 0.00000456
3. 0.0000456
4. 0.000456
5. 456,000
1. What is 9 x 106 in standard form?
2. 9,000,000
3. 90,000,000
4. 900,000,000
5. 9,800,000,000
1. 5.89 x 108 6.4 x 108
2. =
1. 3.87 x 10-4 5.0 x 10-3
2. =
1. 7.21 x 107 3.45 x 108
2. =
1. Which of the following is correctly ordered from greatest to least?
2. 2.0 x 1023.0 x 1064.0 x 10-75.0 x 1012
3. 4.0 x 10-72.0 x 1023.0 x 1065.0 x 1012
4. 3.0 x 1073.0 x 1063.0 x 1023.0 x 10-7
5. 4.0 x 10-75.0 x 10122.0 x 1023.0 x 106
1. Which of the following is correctly ordered from greatest to least?
2. 3.59 x 1064.8 x 1095.4 x 10-56.9 x 10-8
3. 5.49 x 10-56.9 x 10-83.5 x 1064.8 x 109
4. 6.99 x 10-85.4 x 10-53.5 x 1064.8 x 109
5. 1.8 x 1091.5 x 1061.4 x 10-51.9 x 10-8
1. (1 x 10-4 )/( 3 x 10-8 ) is approximately
2. 3,000
3. 30,000
4. 300,000
5. 333,000
1. Identify the number that is not in scientific notation
2. 3.2 x 104
3. 4.0 x 10
4. 52 x 103
5. 9 x 10-2
1. (4.1 x 103 ) x (1.6 x 10-2) =
2. 6.56 x 10
3. 6.56 x 105
4. 6.56 x 10-5
5. 656 x 101
1. What is the magnitude of the number 462,000?
1. 6
2. 3
3. 5
4. 2
1. What is the magnitude of the number .000871
2. 6
3. -6
4. 4
5. -4
1. If M = 817,004.621, what is the smallest power of 10 that will exceed M?
2. 6
3. -6
4. 3
5. 5

Short Constructed Response–Write the correct answer for each question. No partial credit will be given.

For problems 19-23, evaluate and express the result in scientific notation.

1. (2.0 x 103)(2.0 x 106) =______
1. (9 x 10-6) - (3 x 10-6) =______
1. (9.6 x 1012)÷(3.2 x 106) =______
1. (3.3 x 106) + (6.6 x 106) =______
1. (4.2 x 10-1) + (2.4 x 10-1) = ______

Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given.

1. Your body is creating and killing 15 million red blood cells per second.
• Express 15 million in scientific notation.
• How man red blood cells are created in one hour? Express your answer in scientific notation.
• How many are created in one day? Express your answer in scientific notation.
1. There are 18 different animal shapes in the Animal Crackers Cookie Zoo.
• Express this number in scientific notation
• If there are 306 cookies in a package, how many full cookie zoo’s are in the package?
• A case of cookies contains 24 packages. How many sets of animal shapes are there? Express your answer in scientific notation.
1. Every day, 20 banks are robbed. The average take is \$2,500.
• Express the amount stolen in one robbery in scientific notation.
• Express the average amount stolen in one day in scientific notation.
• Express the average amount stolen in one week in scientific notation.
1. A Boeing 747 holds 57,285 gallons of fuel.
• Express the amount of fuel in scientific notation.
• If there are 10 fully fueled Boeing 747s on the tarmac, how much total fuel is in the tanks? Express your answer in scientific notation.
• What is the advantage of using scientific notation for this problem?

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Chapter Questions

1. To make very large and very small numbers easier to read and write.
2. When you want to write very large numbers small, and very small numbers large.
3. Scientific to Standard: Write the coefficient-Add the number of zeros equal to the exponent-Move the decimal the number of places indicated by the exponent.

Standard to Scientific: Write the number without the decimal point-Place the decimal so that the first number is greater than one but less than 10-Count how many places you moved the decimal point; use this as the exponent.

1. First, compare the exponents. If the exponents are different, the coefficients do not matter. Whichever number has the lager exponent is the larger number.
2. Multiply: Multiply the coefficients. Multiply the powers of ten. Combine those results. Put in proper form.

Divide: Divide the coefficients. Divide the powers of ten. Combine those results. Put in proper form.

1. Add or Subtract with same exponents: Add or subtract the coefficients. Rewrite the power of ten. Put in proper form.
2. Add or Subtract with different exponents: Rewrite one of the numbers to have the same exponent as the other number. Add or subtract the coefficients. Rewrite the power of ten. Put in proper form.

Chapter Problems

1. 10
2. 100
3. 1000
4. 10000
5. 100000
6. 108
7. 1017
8. 104
9. 10-11
10. 10-6
11. 1000000000
12. 100000000
13. 10000000
14. 1000000
15. 100000
16. 106
17. 1015
18. 102
19. 10-12
20. 10-5
21. A, E, F
22. 1.303 x 107
23. 4.18 x 105
24. 2.5024 x 107
25. 4.5 x 106
26. 2 x 104
27. 8.7 x 108
28. 3.25 x 10-2
29. 5.64 x 10-5
30. 9.2 x 10-4
31. 1.002 x 10-3
32. 6 x 10-5
33. 9.65784 x 10-3
34. 4.18 x 105
35. 9.8 x 10-4
36. 1.28 x 10-2
37. 5 x 10-4
38. 5.7 x 1015
39. 1.2 x 1014
40. C, D, E, G
41. 4.566 x 106
42. 1.70003 x 107
43. 3.5 x 104
44. 1.078 x 109
45. 4.5607 x 106
46. 9.43 x 1011
47. 5.78 x 10-4
48. 4.598732 x 10-3
49. 5.58744 x 10-7
50. 1.000358 x 10-4
51. 4.5805 x 10-4
52. 8.51 x 10-13
53. 4.92 x 10-6
54. 3 x 108
55. 7.53 x 10-10
56. 1.496 x 108
57. 4 x 107
58. 4.4971 x 109
59. 1550000
60. .00000000002
61. .000000000035
62. 150000000000
63. 602200000000000000000000
64. .0011
65. 750000
66. .0000000009765
67. .0000000127
68. 4560000
69. .000003
70. 678516800
71. .000800045
72. c
73. b
74. .000075
75. 483600000000
76. .0000000000000000001602176
77. 96490
78. 10000000000000
79. .00000055
80. .0008445
81. 5256544000
82. .00001
83. 745207000
84. .0000267
85. 6000500
86. .00400896
1. a
2. d
3. 2
4. 3
5. 6
6. -3
7. -2
8. -6
9. 12
10. 5
11. 2
12. 3
13. 3
14. 6
15. -3
16. -4
17. -5
18. 10
19. 1
20. 4
21. 7.8 x 102, 2.3 x 103, 1.3 x 104, 4.5 x 105
22. 7.0 x 105, 5.0 x 107, 4.0 x 109, 6.0 x 1010
23. 3.3 x 10-4, 7.5 x 10-2, 4.3 x 104, 1.9 x 106
24. 5.5 x 10-25, 2.5 x 10-12, 9.5 x 10-9, 8.2 x 102
25. 2.1 x 104, 3.2 x 104, 5.4 x 104, 9.9x 104
26. 8.2 x 10-6, 9.2 x 10-6,8.2 x 10-5,9.2 x 10-5
27. 4.7 x 103, 6.7 x 104, 6.5 x 105, 8.9 x 107
28. 5.0 x 103, 3.0 x 106, 4.0 x 108, 2.0 x 1012
29. 1.8 x 10-7, 5.7 x 10-3, 9.9 x 105, 4.4 x 106
30. 4.5 x 10-23, 1.9 x 10-10, 3.6 x 10-6, 9.7 x 103
31. 5.0 x 108, 6.7 x 108, 8.9x 108, 9.3 x 108
32. 2.7 x 10-7, 4.5 x 10-7,5.5 x 10-7, 9.0 x 10-7
33. 6 x 104
34. 2 x 109
35. 1.8 x 104
36. 4.8 x 104
37. 2.97 x 105
38. 2.6 x 10-10
39. 4.2 x 103
40. 3.1 x 1010
41. 2.7 x 106
42. 3.5 x 10-3
43. 5 x 10-5
44. 6 x 103
45. 9.856 x 10-17
46. 3.296 x 103
47. 9 x 103
48. 1.6 x 1010
49. 4.2 x 104
50. 2.64 x 104
51. 1.42 x 106
52. 1.32 x 10-9
53. 3.3 x 104
54. 9 x 109
55. 3.75 x 107
56. 2 x 10-10
57. 6 x 10-5
58. 6 x 105
59. 4.0635 x 10-20
60. 1.428571 x 106
61. 4.8 x 105
62. 8.3 x 108
63. 3.4 x 10-6
64. 4.11 x 107
65. 8.35 x 1010
66. 1.11 x 1024
67. 1.331 x 1027
68. 8.9 x 109
69. 9.3 x 106
70. 3.3 x 10-4
71. 2.74 x 108
72. 6.16 x 1012
73. 3.12 x 1023
74. 5.338 x 1024

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NJ Center for Teaching and Learning ~ 1 ~

1. D
2. A
3. C
4. B
5. A
6. D
7. A
8. C
9. C
10. C
11. C
12. D
13. A
14. C
15. A
16. C
17. D
18. A
19. 4.0 x 109
20. 6 x 10-6
21. 3 x 106
22. 9.9 x 106
23. 6.6 x 10-1
24. 1.5 x 107

5.4 x 1010

1.296 x 1012

1. 1.8 x 10

17

4.08 x 102

1. 2.5 x 103

5 x 104

3.5 x 105

1. 5.7285 x 104

5.7285 x 105

The mathematical computations can be done mentally.

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